Video: Cross thiab dot khoom yog dab tsi?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Dot khoom , kev sib cuam tshuam ntawm qhov ntev (x * x, y * y, z * z) Hla khoom , kev sib cuam tshuam ntawm qhov sib txawv (x * y, y * z, z * x, thiab lwm yam)
Hauv qhov no, dab tsi yog cov khoom lag luam thiab cov khoom hla?
Cov dot khoom yog a scalar sawv cev ntawm ob vectors, thiab nws yog siv los nrhiav lub kaum sab xis ntawm ob vectors hauv txhua qhov chaw seem. Cov cross khoom yog a vector orthogonal rau peb-dimensional vectors thiab, thiab tuaj yeem siv los txiav txim siab thaj tsam lossis ntim ntawm parallelogram txhais los ntawm,, thiab.
Tom qab ntawd, lo lus nug yog, qhov khoom dot txhais li cas? Hauv lej, the dot khoom los yog khoom scalar yog ib qho kev ua algebraic uas siv ob qhov sib npaug ntawm qhov sib npaug ntawm cov lej (feem ntau ua haujlwm vectors) thiab xa rov qab ib tus lej. Geometrically, nws yog khoom ntawm Euclidean qhov loj ntawm ob lub vectors thiab cosine ntawm lub kaum sab xis ntawm lawv.
Hauv qhov no, dab tsi yog qhov khoom ntawm ob lub vectors?
Cov cross khoom a × b yog txhais ua a vector c uas yog perpendicular (orthogonal) rau ob qho tib si a thiab b, nrog rau kev taw qhia los ntawm txoj cai sab xis thiab qhov loj sib npaug rau thaj tsam ntawm parallelogram uas cov duab ncua.
Yuav ua li cas koj nrhiav tau tus ntoo khaub lig thiab dot khoom?
- Nrhiav tus ntoo khaub lig khoom u x v if.
- Kev tawm dag zog. Nrhiav koj x v thaum.
- Cia koj thiab v ua vectors thiab xav txog qhov parallelogram uas ob vectors ua. Ces. ||u x v|| = Thaj tsam ntawm Parallelogram. thiab cov kev taw qhia ntawm u x v yog lub kaum sab xis rau lub parallelogram uas ua raws li txoj cai sab xis.
- Kev tawm dag zog. Nrhiav j x k thiab i x k.
Pom zoo:
Dab tsi yog cov khoom ntawm dot khoom?
Cov khoom dot ua tiav cov khoom nram qab no yog tias a, b, thiab c yog cov vectors tiag tiag thiab r yog scalar. Commutative: uas ua raws li lub ntsiab lus (θ yog lub kaum sab xis ntawm a thiab b): Distributive tshaj vector ntxiv: Bilinear: Scalar multiplication:
Dab tsi yog qhov zoo sib xws ntawm cov khoom thiab cov khoom sib txuas?
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